Does matter made out of ions radiate more energy than matter made out of atoms? I hope someone could correct the mistakes I'm making in my speech. Thanks.
Some say that when matter heats up, its atoms start accelerating faster in random directions exchanging energy by bumping into eachother.
Accelerating atoms inside a material are supposed to emit EM waves. So when matter heats up, it starts emiting more energy as EM radiation. If we accelerate a free charge it starts emiting light. The same is true for accelerating ions which are just atoms with an unbalanced charges. Does the same happen for atoms if they are not bound in a material?
That seems to me like both electrons and protons emit light as they accelerate in the same directions inside the atom which is bound to a material. But its EM waves destructively interfere so they should emit nothing. But wouldn't that mean they lose energy anyways because they've all emited it? 
Other people say that heated atoms don't really accelerate but the electrons jump to a higher energy state, and when they fall down, they emit light. But that would mean that accelerating ions then shouldn't emit EM waves.
What is correct interpretation then?
Both can't be correct.
 A: Accelerated charged particles emit electromagnetic radiation. The emitted power is proportional to the square of the acceleration. Given a fixed charge, then an accelerating Lorentz force produces an acceleration inversely proportional to mass and so  radiated power is inversely proportional to the square of the mass.
As ions are much more massive than free electrons, then their radiative output (by this mechanism) can usually be neglected. There is no question of constructive or destructive interference here because there is no reason that the light emitted by separate particles should have any particular phase relationship.
Heated atoms and ions do move faster and heat may result in electrons occupying higher energy states in both (if the ions have any remaining electrons). You appear to be confused between two mechanisms of producing radiation. One consists of acceleration of free charged particles - free-free emission that could be thermal in nature or caused by external fields; the other is transitions within atoms/ions - bound-bound transitions between bound energy states.
In general both these things (and bound-free and free-bound radiation) are occurring.
A: The optical vibrational modes of salts are in the infrared. Those absorb and reflect strongly (Reststrahlen), so they will also radiate. In the same region of the spectrum, covalent materials can be transparent, so the black-body radiation will be low.
